Symmetry and monotonicity results for solutions of vectorial p-stokes systems

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URI: https://hdl.handle.net/10481/80910
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Autor
López Soriano, Rafael
Editorial
American Mathematical Society
Materia
p-Stokes system
 
p-Laplacian system
 
Comparison principle
 
Moving plane method
 
Fecha
2021-12-20
Referencia bibliográfica
Published version: López-Soriano, R., Montoro, L., & Sciunzi, B. (2023). Symmetry and monotonicity results for solutions of vectorial 𝑝-Stokes systems. Transactions of the American Mathematical Society. [https://doi.org/10.1090/tran/8867]
Patrocinador
Spanish Government PID2019-106122GB-I00/AEI/10.3039/501100011033 Ministry of Education, Universities and Research (MIUR) Research Projects of National Relevance (PRIN) 2017JPCAPN Spanish Government PDI2019-110712GB-100
Resumen
In this paper we shall study qualitative properties of a p-Stokes type system, namely -Delta pu = - div(|Du|p-2Du) = f (x, u) in omega, where Delta p is the p-Laplacian vectorial operator. More precisely, under suitable assumptions on the domain omega and the function f, it is deduced that system solutions are symmetric and monotone. Our main results are derived from a vectorial version of the weak and strong comparison principles, which enable to proceed with the moving-planes technique for systems. As far as we know, these are the first qualitative kind results involving vectorial operators.
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